Proportionality>Solving Problems with Similar Shapes and Scale Drawings(TEKS.Math.7.5.C)
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Texas 7th Grade Math › Proportionality>Solving Problems with Similar Shapes and Scale Drawings(TEKS.Math.7.5.C)
On a blueprint with scale 1:50, a room measures 6 cm by 8 cm. What are the actual room dimensions?
0.12 m × 0.16 m
3 m × 4 m
30 m × 40 m
3.6 m × 4.8 m
Explanation
The linear scale factor is $k=50$. Actual lengths: 6×50=300 cm=3 m and 8×50=400 cm=4 m. So 3 m × 4 m. Distractors divide by 50, confuse cm-to-m conversion, or use the wrong factor.
A model car is built at a scale of 1:24. If the actual car is 4.8 m long, what is the length of the model?
20 cm
24 cm
2 m
4.8 cm
Explanation
For model:actual, the linear scale factor is $k=\tfrac{1}{24}$. Model length = 4.8×(1/24) = 0.2 m = 20 cm. Distractors multiply by 24, ignore unit conversion, or use an incorrect factor.
Two similar pentagons have perimeters 30 cm (smaller) and 45 cm (larger). What is the scale factor from the smaller to the larger pentagon?
1
2
2
15
Explanation
Perimeters scale linearly with $k$. So $k=\dfrac{45}{30}=1.5$. Choosing 0.67 reverses the ratio, 2.25 uses an area-type factor ($k^2$), and 15 confuses a length with a scale factor.